(1932) "The distribution of the index in a bivariate Normal distribution".

It may be thought of as an analogue on the torus of the bivariate normal distribution.

He also discovered the properties of the bivariate normal distribution and its relationship to regression analysis.

Note that is the cumulative distribution function of the bivariate normal distribution.

An example of a bivariate Cauchy distribution can be given by:

Regression towards the mean can be defined for any bivariate distribution with identical marginal distributions.

Not all such bivariate distributions show regression towards the mean under this definition.

However, all such bivariate distributions show regression towards the mean under the other definition.

"On some sets of sufficent conditions leading to the normal bivariate distribution", Sankhya, 6 (1943) 399 - 406.

For most other bivariate distributions this is not true.